INTEGRATION OF STOCHASTIC DIFFERENTIAL EQUATIONS ON SUPERCOMPUTERS

A GENERIC SOFTWARE PACKAGE FOR NUMERICAL SIMULATION OF LTO RULE STOCHASTIC DIFFERENTIAL EQUATIONS INTENDED FOR USE ON SUPERCOMPUTERS IS DESCRIBED. MANY PROBLEMS OF PHYSICAL INTEREST ARE INTRINSICALLY LARGE DIMENSIONAL WHICH ALSO ENHANCES THE ATTRACTIVENESS OF VECTOR/PARALLEL PROCESSING MACHINES. PROBLEMS OF STABILITY ARE MORE SERIOUS THAN IN ORDINARY DIFFERENTIAL EQUATIONS AND ARE DUE TO THE UNBOUNDED VARIATION OF BROWNIAN MOTION. THE FOLLOWING APPROACHES TO ENHANCE STABILITY, ACCURACY AND EFFICIENCY WILL BE PURSUED. 1. IMPLICIT ALGORITHMS (E.G. TRAPEZOIDAL RULE); 2. VARIANCE REDUCTION METHODS (E.G. ANTITHETIC VARIATES); 3. VARIABLE TIME STEP ALGORITHMS; AND 4. NEW METHODS FOR GENERATING RANDOM NUMBERS.